Measured on the Richter scale, the magnitude of an earthquake of intensity \( I \) is defined as \( R=\log \left(I / I_{0}\right) \) where \( I_{0} \) is a minimum level for comparison. What is the Richter scale reading for the earthquake for which \( I=73,000,000 \mathrm{I}_{0} \) ? The magnitude of the earthquake was (Simplify your answer. Round to one decimal place as needed.)

To find the Richter scale reading for the earthquake with intensity \( I = 73,000,000 I_{0} \), we can use the formula: \[ R = \log \left( \frac{I}{I_{0}} \right) \] Substituting the values, we have: \[ R = \log \left( \frac{73,000,000 I_{0}}{I_{0}} \right) = \log(73,000,000) \] Now, we calculate \( \log(73,000,000) \). This can be written as: \[ R = \log(7.3 \times 10^7) = \log(7.3) + \log(10^7) \] Using the logarithm properties, we have \( \log(10^7) = 7 \). For \( \log(7.3) \), if we refer to a calculator, we can find that \( \log(7.3) \approx 0.8633 \). Now summing these values: \[ R \approx 0.8633 + 7 = 7.8633 \] Rounding to one decimal place: \[ R \approx 7.9 \] Thus, the magnitude of the earthquake was approximately \( 7.9 \).